Question

The graph of $x^2+y=10$ and the graph of $x+y=10$ intersect in two points, what is the distance between the points?

• A. $\sqrt{1}$
• B. 1
• C. $\sqrt{2}$
• D. 2

Answer 1

The correct option is C $\sqrt{2}$

$x^2+y=10$ & $x+y=10$ Enter sects

$\Rightarrow y=10-x^2$ & $y=10-x\Rightarrow 10-x^2=10-x$

$\Rightarrow x=0,1$ & corresponding $y=10,9$

$\therefore$ pt.s are $(0,10)\&(1,9)$ & distance is

$\sqrt{(0-1{)}^2+(10-9{)}^2}=\sqrt{2}$